Prime Mystery: The Life and Mathematics of Sophie Germain: Revolutionary Mathematician

Description

This biography of the mathematician, Sophie Germain, paints a rich portrait of a brilliant and complex woman, the mathematics she developed, her associations with Gauss, Legendre, and other leading researchers, and the tumultuous times in which she lived. Sophie Germain stood right between Gauss and Legendre, and both publicly recognized her scientific efforts. Unlike her female predecessors and contemporaries, Sophie Germain was an impressive mathematician and made lasting contributions to both number theory and the theories of plate vibrations and elasticity. She was able to walk with ease across the bridge between the fields of pure mathematics and engineering physics. Though isolated and snubbed by her peers, Sophie Germain was the first woman to win the prize of mathematics from the French Academy of Sciences. She is the only woman who contributed to the proof of Fermat’s Last Theorem. In this unique biography, Dora Musielak has done the impossible?she has chronicled Sophie Germain’s brilliance through her life and work in mathematics, in a way that is simultaneously informative, comprehensive, and accurate. Preface to the Second Edition Preface to the First Edition Acknowledgements Contents 1 Unforgettable Childhood Primary Education Revolutionary Mathematicians Coming of Age Through the Terror Institut de France: Science Above All 2 Lessons from l’École Polytechnique Lagrange’s Lecture Notes 1797–1799 M. LeBlanc Metamorphoses into Mlle Germain A Young Scholar Emerges 3 Sophie’s Sublime Arithmetica Number Theory: From Diophantus to Gauss Sophie Germain and Carl Friedrich Gauss How Napoléon’s Invasion Led to Unmasking M. Le Blanc Sophie Germain Tackles the Law of Quadratic Reciprocity Gauss: Mathematical Astronomer Gauss and Legendre: A Matter of Priority 4 Chladni and His Acoustic Experiments The Prize of Mathematics, 1809 5 Euler and the Bernoullis Euler and the Mechanics of Elastic Bodies Foundation of Elasticity Theories Sound and Vibrating Bodies 6 Germain and Her Biharmonic Equation First Hypothesis Second Attempt: More Disappointment Paris in 1814 Winning the Grand Prix de Mathématiques Confronting a Rival The Germain-Lagrange Equation 7 Experiments with Vibrating Plates Sophie Germain’s Experimental Research 8 Elasticity Theory After Germain Navier’s Bending Equation Cauchy and His Mathematical Formalism Poisson and an Incorrect Prediction Poisson-Germain-Navier Public Dispute Kirchhoff’s Plate Theory Ritz Method to Model Chladni’s Plates 9 Germain and Fermat’s Last Theorem Pierre de Fermat Euler and Fermat’s Theorems Legendre Proposes a Contest to Prove FLT Sophie Germain’s Theorem Unexpected Revelation Germain’s Research to Prove Fermat’s Last Theorem Fermat’s Last Theorem After Germain The Fermat-Wiles Theorem Unsolved Problems in Number Theory 10 Pensées de Germain 11 Friends, Rivals, and Mentors Introduction Carl Friedrich Gauss (1777–1855) Joseph-Louis Lagrange (1736–1813) Adrien-Marie Legendre (1752–1833) Jean-Baptiste-Joseph Fourier (1768–1830) Siméon-Denis Poisson (1781–1840) Claude-Louis-Marie-Henri Navier (1785–1836) Jean-Baptiste Joseph Delambre (1749–1822) Augustin-Louis Cauchy (1789–1857) Guglielmo Libri, Count de Bagnano (1803–1869) Leonhard Euler (1707–1783) Archimedes of Syracuse (c. 287–212 B.C.) 12 The Last Years Reaching Out to Gauss, One Last Time Glorious Summer of 1830 Germain’s Last Publications 13 Unanswered Questions 14 Princess of Mathematics Women and Science Education Sophie Germain Legacy Germain-Gauss Correspondance Sophie Germain Timeline Illustration Credits Bibliography Index